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TS EAMCET · Maths · Vector Algebra

\(\overrightarrow{\mathbf{a}} \cdot \hat{\mathbf{i}}=\overrightarrow{\mathbf{a}} \cdot(2 \hat{\mathbf{i}}+\hat{\mathbf{j}})=\overrightarrow{\mathbf{a}}(\hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}})=1\), then \(\overrightarrow{\mathbf{a}}\) is equal to :

  1. A \(\hat{\mathbf{i}}-\hat{\mathbf{k}}\)
  2. B \(1 / 3(3 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\hat{\mathbf{k}})\)
  3. C \(1 / 3(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})\)
  4. D \(1 / 3(3 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+\hat{\mathbf{k}})\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(1 / 3(3 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+\hat{\mathbf{k}})\)

Step-by-step Solution

Detailed explanation

Let \(\overrightarrow{\mathbf{a}}=a_1 \hat{\mathbf{i}}+a_2 \hat{\mathbf{j}}+a_3 \hat{\mathbf{k}}\) \(\because \quad \overrightarrow{\mathbf{a}} \cdot \hat{\mathbf{i}}=1\)…